Airfoil shape for a compressor

ABSTRACT

An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in a scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

RELATED APPLICATIONS

The present application is related to the following commonly assigned applications: Ser. No. ______ (Docket No. 277752 (1011)); Ser. No. ______ (Docket No. 277754 (1013)); Ser. No. ______ (Docket No. 277765 (1014)); Ser. No. ______ (Docket No. 277784 (1012)); Ser. No. ______ (Docket No. 277913 (1016)); Ser. No. ______ (Docket No. 278957 (1015)); Ser. No. ______ (Docket No. 279003 (1018)); Ser. No. ______ (Docket No. 279149 (1019)); Ser. No. ______ (Docket No. 280088 (1020)); Ser. No. ______ (Docket No. 280098 (1021)), filed concurrently herewith.

TECHNICAL FIELD

The present application and the resultant patent relate generally to gas turbine engines and more particularly relates to an airfoil profile or airfoil shape for use in a compressor.

BACKGROUND OF THE INVENTION

In a gas turbine engine, many system requirements should be met at each stage of the flow path therethrough to meet design goals. These design goals include, but are not limited to, overall improved efficiency, a reduction in vibratory response, improved airfoil loading capability, and the like. For example, a compressor airfoil profile should achieve thermal and mechanical operating requirements for a particular stage in the compressor. Moreover, component lifetime, reliability, and cost targets also should be met.

SUMMARY OF THE INVENTION

According to one aspect of the present application, an article of manufacture is provided with a nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

According to another aspect of the present application, an article of manufacture is provided with a suction-side nominal airfoil profile substantially in accordance with the suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y, and Z coordinate values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil profile.

According to yet another aspect of the present application, a compressor is provided with a number of stator vanes, each of the stator vanes including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with the suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape.

These and other features and improvements of the present application and the resultant patent will become apparent to one of ordinary skill in the art upon review of the following detailed description when taken in conjunction with the several drawings and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a gas turbine engine including a compressor, a combustor, a turbine, and a load.

FIG. 2 is a schematic diagram of a compressor with multiple stages and a flow path therethrough.

FIG. 3 is a perspective view of a stator vane airfoil as may be described herein.

FIG. 4 is a cross-sectional view of the stator vane airfoil taken along line 4-4 of FIG. 3.

DETAILED DESCRIPTION

Referring now to the drawings, in which like numerals refer to like elements throughout the several views, FIG. 1 shows a schematic view of gas turbine engine 10 as may be used herein. The gas turbine engine 10 may include a compressor 15. The compressor 15 compresses an incoming flow of air 20. The compressor 15 delivers the compressed flow of air 20 to a combustor 25. The combustor 25 mixes the compressed flow of air 20 with a pressurized flow of fuel 30 and ignites the mixture to create a flow of combustion gases 35. Although only a single combustor 25 is shown, the gas turbine engine 10 may include any number of the combustors 25 arranged in a circumferential array or otherwise. The flow of combustion gases 35 is delivered in turn to a turbine 40. The flow of combustion gases 35 drives the turbine 40 so as to produce mechanical work. The mechanical work produced in the turbine 40 drives the compressor 15 via a shaft 45 and an external load 50 such as an electrical generator and the like.

The gas turbine engine 10 may use natural gas, liquid fuels, various types of syngas, and/or other types of fuels and blends thereof. The gas turbine engine 10 may be any one of a number of different gas turbine engines offered by General Electric Company of Schenectady, New York, including, but not limited to, those such as a 7 or a 9 series heavy duty gas turbine engine and the like. The gas turbine engine 10 may have different configurations and may use other types of components. Other types of gas turbine engines also may be used herein. Multiple gas turbine engines, other types of turbines, and other types of power generation equipment also may be used herein together.

FIG. 2 shows an example of the compressor 15. The compressor 15 may include a number of compressor stages with an axial compressor flow path 55 therethrough. As one non-limiting example only, the compressor flow path 55 may include about eighteen rotor/stator stages. The exact number of rotor and stator stages, however, may be a matter of engineering design choice and may be more or less than the illustrated eighteen stages. It is to be understood that any number of rotor and stator stages may be provided herein.

Each stage of the compressor 15 may include a number of circumferentially spaced rotor blades 60 mounted on a rotor wheel 65 and a number of circumferentially spaced stator vanes 70 attached to a static compressor case 75. Each of the rotor wheels 65 may be attached to an aft drive shaft 80, which may be connected to the turbine section of the engine. The rotor blades and stator vanes may lie in the flow path 55 of the compressor 15. The direction of airflow through the compressor flow path 55 flows generally from left to right in FIG. 2. Other components and other configurations may be used herein.

The compressor rotor blades 60 impart kinetic energy to the airflow and therefore bring about a desired pressure rise. Directly following the rotor blades 60 may be a stage of the compressor stator vanes 70. However, in some designs the stator vanes may precede the rotor blades. Both the rotor blades and stator vanes turn the airflow, slow the airflow velocity (in the respective airfoil frame of reference), and yield a rise in the static pressure of the airflow. Typically, multiple rows of rotor/stator stages are arranged in axial flow compressors to achieve a desired discharge to inlet pressure ratio. Each rotor blade and stator vane includes an airfoil, and these airfoils can be secured to rotor wheels or a stator case by an appropriate attachment configuration, often known as a “root,” “base” or “dovetail”. In addition, the compressor 15 also may include inlet guide vanes (IGV's) 85, variable stator vanes (VSV's) 90, and exit or exhaust guide vanes (EGV's) 95. All of these blades and vanes have airfoils that act on the medium (e.g., air) passing through the compressor flow path 55. Other components and other configurations may be used herein.

The rotor blades 60 and stator vanes 70 are merely exemplary of the stages of the compressor 15 described herein. In addition, each rotor blade 60, stator vane 70, inlet guide vane 85, variable stator vane 90, and exit guide vane 95 may be considered an article of manufacture. Further, the article of manufacture may include a stator vane configured for use with a compressor 15.

FIG. 3 shows an example of a stator vane 100 as may be described herein. In this example, the stator vane 100 includes an airfoil 105. Each of the stator vanes 100 may have an airfoil profile at any cross-section from an airfoil root 110 to an airfoil tip 120. The airfoil 105 may connect to a mounting base 130, which also may be referred to as a dovetail. The mounting base 130 fits into a complementary shaped groove or slot in case 75. Examples of the compressor 15 may include a variety of blades 60 and vanes 70, 85, 90, 95 arranged in multiple stages.

Referring to FIG. 4, the airfoil 105 may have a suction side 140 and a pressure side 150. The suction side 140 may be located on the opposing side of the airfoil 105 from the pressure side 150. Thus, each stator vane 60 may have an airfoil profile at any cross-section in the shape of the airfoil 105. The airfoil 105 also may include a leading edge 160 and a trailing edge 170 and with a chord length 180 extending therebetween. The root 110 of the airfoil 105 corresponds to the lowest non-dimensional Z value of scalable TABLE 1. The tip 120 of the airfoil 105 corresponds to the highest non-dimensional Z value of scalable TABLE 1. An airfoil 105 may extend beyond the compressor flowpath and may be tipped to achieve the desired endwall clearances. By way of example only, the airfoil may have a height from about one (1) inch to about twenty (20) inches (about 2.54 centimeters to about 50.8 centimeters) or more. Any specific airfoil height may be used herein as desired in a specific application. Other components and other configurations may be used herein.

The compressor flow path 55 requires airfoils 105 that meet system requirements of aerodynamic and mechanical blade/vane loading and efficiency. For example, it is desirable that the airfoils 105 are designed to reduce the vibratory response or vibratory stress response of the respective blades and/or vanes. Materials such as high strength alloys, non-corrosive alloys, and/or stainless steels may be used in the blades and/or vanes. To define the airfoil shape of each blade airfoil and/or vane airfoil, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. These unique loci of points meet the requirements for stage efficiency and may be arrived at by iteration between aerodynamic and mechanical loadings so as to enable the turbine and compressor to run in an efficient, safe, reliable, and smooth manner. These points are unique and specific to the system. The locus that defines the airfoil profile includes a set of points with X, Y, and Z coordinates relative to a reference origin coordinate system. The three-dimensional Cartesian coordinate system of X, Y, and Z values given in scalable TABLE 1 below defines the profile of the stator vane airfoil at various locations along its length. The scalable TABLE 1 lists data for a non-coated airfoil. The envelope/tolerance for the coordinates may be about +/−5% of the chord length 180 in a direction normal to any airfoil surface location or about +/−0.25 inches (about 6.36 millimeters) in a direction normal to any airfoil surface location. However, tolerances of about +/−0.15 inches to about +/−0.25 inches (about 6.36 millimeters), or about +/−3% to about +/−5% in a direction normal to an airfoil surface location may also be used, as desired in the specific application.

A point data origin 190 may be the mid-point of the suction or pressure side of the base or tip of the airfoil, the leading edge or trailing edge of the base of the airfoil, or any other suitable location as desired. The coordinate values for the X, Y, and Z coordinates are set forth in non-dimensionalized units in scalable TABLE 1, although other units of dimensions may be used when the values are appropriately converted. As one example only, the Cartesian coordinate values of X, Y, and Z may be convertible to dimensional distances by multiplying the X, Y, and Z values by a constant number (e.g., 100). The number, used to convert the non-dimensional values to dimensional distances, may be a fraction (e.g., ½, ¼, etc.), decimal fraction (e.g., 0.5, 1.5, 10.25, etc.), integer (e.g., 1, 2, 10, 100, etc.), a mixed number (e.g., 11/2, 101/4, etc.), and the like. The dimensional distances may be in any suitable format (e.g., inches, feet, millimeters, centimeters, meters, etc.) As one non-limiting example only, the Cartesian coordinate system has orthogonally-related X, Y, and Z axes and the X axis may lie generally parallel to the compressor rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward the aft, i.e., exhaust end of the turbine. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the rotor blade tip or stator vane base. All the values in scalable TABLE 1 are given at room temperature and are unfilleted.

By defining X and Y coordinate values at selected locations in a Z direction (or height) normal to the X, Y plane, the profile section or airfoil shape of the airfoil, at each Z height along the length of the airfoil may be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each Z height may be fixed. The airfoil profiles of the various surface locations between each Z height may be determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The values in TABLE 1 may be generated and shown from zero to four or more decimal places for determining the profile of the airfoil. As the airfoil heats up the associated stress and temperature may cause a change in the X, Y, and Z values. Accordingly, the values for the profile given in TABLE 1 represent ambient, non-operating or non-hot conditions (e.g., room temperature) and may be for an uncoated airfoil.

There are typical manufacturing tolerances as well as optional coatings which may be accounted for in the actual profile of the airfoil. Each section may be joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in TABLE 1 below. Accordingly, a distance of about +/−5% of chord length and/or +/−0.25 inches (about 6.36 millimeters) in a direction normal to a surface location along the airfoil profile defines an airfoil profile envelope for this particular airfoil design and compressor, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the TABLE 1 below at the same temperature. Additionally, a distance of about +/−5% of a chord length in a direction normal to an airfoil surface location along the airfoil profile also may define an airfoil profile envelope for this particular airfoil design. The data is scalable and the geometry pertains to all aerodynamic scales, at, above and/or below about 3,000 RPM. The stator vane airfoil design is robust to this range of variation without impairment of mechanical and aerodynamic functions.

The coordinate values given in scalable TABLE 1 below provide the nominal profile for exemplary stages of a compressor stator vane. Specifically, a fourth stage stator vane of, for example, a 7HA.01 compressor, a 9HA.01 compressor, and the like:

TABLE 1 SUCTION SIDE PRESSURE SIDE X Y Z X Y Z −1.1805 1.1929 −0.3770 1.8944 −1.9485 −0.3770 −1.1869 1.1895 −0.3770 1.8947 −1.9476 −0.3770 −1.1939 1.1828 −0.3770 1.8953 −1.9460 −0.3770 −1.2004 1.1727 −0.3770 1.8964 −1.9426 −0.3770 −1.2056 1.1593 −0.3770 1.8975 −1.9356 −0.3770 −1.2097 1.1406 −0.3770 1.8969 −1.9246 −0.3770 −1.2121 1.1160 −0.3770 1.8892 −1.9063 −0.3770 −1.2121 1.0851 −0.3770 1.8692 −1.8890 −0.3770 −1.2092 1.0476 −0.3770 1.8403 −1.8683 −0.3770 −1.2031 1.0036 −0.3770 1.8042 −1.8423 −0.3770 −1.1934 0.9526 −0.3770 1.7574 −1.8085 −0.3770 −1.1793 0.8929 −0.3770 1.7034 −1.7694 −0.3770 −1.1602 0.8246 −0.3770 1.6459 −1.7275 −0.3770 −1.1362 0.7478 −0.3770 1.5813 −1.6803 −0.3770 −1.1073 0.6629 −0.3770 1.5097 −1.6276 −0.3770 −1.0738 0.5698 −0.3770 1.4312 −1.5693 −0.3770 −1.0333 0.4698 −0.3770 1.3494 −1.5081 −0.3770 −0.9886 0.3666 −0.3770 1.2644 −1.4436 −0.3770 −0.9388 0.2608 −0.3770 1.1765 −1.3757 −0.3770 −0.8831 0.1527 −0.3770 1.0858 −1.3042 −0.3770 −0.8218 0.0422 −0.3770 0.9925 −1.2287 −0.3770 −0.7546 −0.0705 −0.3770 0.8969 −1.1490 −0.3770 −0.6809 −0.1853 −0.3770 0.7992 −1.0647 −0.3770 −0.6001 −0.3017 −0.3770 0.6998 −0.9758 −0.3770 −0.5149 −0.4148 −0.3770 0.6020 −0.8853 −0.3770 −0.4258 −0.5240 −0.3770 0.5056 −0.7933 −0.3770 −0.3330 −0.6294 −0.3770 0.4106 −0.6998 −0.3770 −0.2366 −0.7314 −0.3770 0.3169 −0.6051 −0.3770 −0.1367 −0.8300 −0.3770 0.2245 −0.5090 −0.3770 −0.0334 −0.9251 −0.3770 0.1334 −0.4117 −0.3770 0.0733 −1.0169 −0.3770 0.0437 −0.3130 −0.3770 0.1833 −1.1054 −0.3770 −0.0445 −0.2129 −0.3770 0.2967 −1.1904 −0.3770 −0.1311 −0.1116 −0.3770 0.4127 −1.2715 −0.3770 −0.2161 −0.0090 −0.3770 0.5313 −1.3486 −0.3770 −0.2996 0.0948 −0.3770 0.6484 −1.4193 −0.3770 −0.3791 0.1961 −0.3770 0.7636 −1.4842 −0.3770 −0.4551 0.2946 −0.3770 0.8765 −1.5437 −0.3770 −0.5277 0.3901 −0.3770 0.9864 −1.5985 −0.3770 −0.5969 0.4827 −0.3770 1.0931 −1.6491 −0.3770 −0.6625 0.5724 −0.3770 1.1964 −1.6961 −0.3770 −0.7249 0.6589 −0.3770 1.2958 −1.7399 −0.3770 −0.7849 0.7417 −0.3770 1.3914 −1.7808 −0.3770 −0.8396 0.8172 −0.3770 1.4785 −1.8174 −0.3770 −0.8892 0.8857 −0.3770 1.5571 −1.8500 −0.3770 −0.9333 0.9469 −0.3770 1.6271 −1.8785 −0.3770 −0.9726 1.0008 −0.3770 1.6928 −1.9051 −0.3770 −1.0073 1.0470 −0.3770 1.7498 −1.9280 −0.3770 −1.0374 1.0855 −0.3770 1.7937 −1.9456 −0.3770 −1.0642 1.1176 −0.3770 1.8289 −1.9595 −0.3770 −1.0879 1.1434 −0.3770 1.8555 −1.9693 −0.3770 −1.1089 1.1633 −0.3770 1.8765 −1.9670 −0.3770 −1.1270 1.1777 −0.3770 1.8864 −1.9603 −0.3770 −1.1420 1.1870 −0.3770 1.8912 −1.9544 −0.3770 −1.1543 1.1923 −0.3770 1.8931 −1.9511 −0.3770 −1.1651 1.1947 −0.3770 1.8940 −1.9493 −0.3770 −1.1740 1.1946 −0.3770 −1.1859 1.2312 0.0000 1.8976 −1.7452 0.0000 −1.1920 1.2276 0.0000 1.8979 −1.7444 0.0000 −1.1986 1.2210 0.0000 1.8985 −1.7428 0.0000 −1.2046 1.2110 0.0000 1.8995 −1.7395 0.0000 −1.2094 1.1979 0.0000 1.9006 −1.7328 0.0000 −1.2130 1.1796 0.0000 1.8999 −1.7221 0.0000 −1.2146 1.1556 0.0000 1.8918 −1.7046 0.0000 −1.2137 1.1257 0.0000 1.8718 −1.6885 0.0000 −1.2096 1.0893 0.0000 1.8434 −1.6685 0.0000 −1.2020 1.0467 0.0000 1.8080 −1.6436 0.0000 −1.1906 0.9976 0.0000 1.7620 −1.6111 0.0000 −1.1748 0.9401 0.0000 1.7090 −1.5735 0.0000 −1.1540 0.8745 0.0000 1.6525 −1.5333 0.0000 −1.1282 0.8008 0.0000 1.5891 −1.4879 0.0000 −1.0972 0.7192 0.0000 1.5188 −1.4373 0.0000 −1.0612 0.6300 0.0000 1.4416 −1.3814 0.0000 −1.0179 0.5345 0.0000 1.3612 −1.3225 0.0000 −0.9704 0.4362 0.0000 1.2777 −1.2606 0.0000 −0.9179 0.3355 0.0000 1.1912 −1.1955 0.0000 −0.8596 0.2329 0.0000 1.1019 −1.1269 0.0000 −0.7956 0.1283 0.0000 1.0100 −1.0545 0.0000 −0.7257 0.0219 0.0000 0.9157 −0.9781 0.0000 −0.6494 −0.0861 0.0000 0.8194 −0.8976 0.0000 −0.5663 −0.1954 0.0000 0.7212 −0.8128 0.0000 −0.4789 −0.3019 0.0000 0.6243 −0.7266 0.0000 −0.3881 −0.4045 0.0000 0.5288 −0.6390 0.0000 −0.2939 −0.5036 0.0000 0.4345 −0.5502 0.0000 −0.1965 −0.5992 0.0000 0.3413 −0.4601 0.0000 −0.0961 −0.6915 0.0000 0.2492 −0.3690 0.0000 0.0073 −0.7805 0.0000 0.1582 −0.2767 0.0000 0.1137 −0.8664 0.0000 0.0684 −0.1832 0.0000 0.2229 −0.9491 0.0000 −0.0203 −0.0885 0.0000 0.3351 −1.0287 0.0000 −0.1079 0.0073 0.0000 0.4496 −1.1048 0.0000 −0.1944 0.1042 0.0000 0.5663 −1.1773 0.0000 −0.2798 0.2021 0.0000 0.6813 −1.2439 0.0000 −0.3613 0.2976 0.0000 0.7941 −1.3052 0.0000 −0.4393 0.3904 0.0000 0.9044 −1.3614 0.0000 −0.5140 0.4804 0.0000 1.0119 −1.4132 0.0000 −0.5853 0.5675 0.0000 1.1161 −1.4611 0.0000 −0.6531 0.6519 0.0000 1.2168 −1.5055 0.0000 −0.7177 0.7333 0.0000 1.3139 −1.5470 0.0000 −0.7798 0.8112 0.0000 1.4071 −1.5857 0.0000 −0.8364 0.8824 0.0000 1.4920 −1.6204 0.0000 −0.8876 0.9468 0.0000 1.5686 −1.6512 0.0000 −0.9333 1.0045 0.0000 1.6368 −1.6783 0.0000 −0.9740 1.0552 0.0000 1.7009 −1.7036 0.0000 −1.0098 1.0986 0.0000 1.7564 −1.7253 0.0000 −1.0409 1.1347 0.0000 1.7992 −1.7419 0.0000 −1.0685 1.1646 0.0000 1.8334 −1.7552 0.0000 −1.0930 1.1885 0.0000 1.8593 −1.7646 0.0000 −1.1144 1.2068 0.0000 1.8798 −1.7628 0.0000 −1.1328 1.2197 0.0000 1.8895 −1.7566 0.0000 −1.1480 1.2278 0.0000 1.8944 −1.7509 0.0000 −1.1603 1.2322 0.0000 1.8963 −1.7477 0.0000 −1.1710 1.2338 0.0000 1.8972 −1.7461 0.0000 −1.1797 1.2332 0.0000 −1.1909 1.2664 0.3474 1.9008 −1.5581 0.3474 −1.1967 1.2627 0.3474 1.9011 −1.5573 0.3474 −1.2029 1.2561 0.3474 1.9018 −1.5558 0.3474 −1.2086 1.2462 0.3474 1.9027 −1.5526 0.3474 −1.2128 1.2332 0.3474 1.9038 −1.5459 0.3474 −1.2158 1.2153 0.3474 1.9030 −1.5355 0.3474 −1.2167 1.1918 0.3474 1.8948 −1.5186 0.3474 −1.2148 1.1627 0.3474 1.8749 −1.5032 0.3474 −1.2095 1.1274 0.3474 1.8469 −1.4841 0.3474 −1.2005 1.0861 0.3474 1.8120 −1.4602 0.3474 −1.1876 1.0385 0.3474 1.7667 −1.4291 0.3474 −1.1700 0.9831 0.3474 1.7144 −1.3931 0.3474 −1.1474 0.9199 0.3474 1.6588 −1.3546 0.3474 −1.1196 0.8490 0.3474 1.5962 −1.3111 0.3474 −1.0865 0.7704 0.3474 1.5269 −1.2626 0.3474 −1.0480 0.6848 0.3474 1.4509 −1.2090 0.3474 −1.0022 0.5933 0.3474 1.3717 −1.1525 0.3474 −0.9521 0.4993 0.3474 1.2895 −1.0930 0.3474 −0.8970 0.4032 0.3474 1.2044 −1.0303 0.3474 −0.8362 0.3055 0.3474 1.1165 −0.9643 0.3474 −0.7697 0.2062 0.3474 1.0259 −0.8946 0.3474 −0.6973 0.1054 0.3474 0.9329 −0.8213 0.3474 −0.6186 0.0033 0.3474 0.8376 −0.7441 0.3474 −0.5331 −0.0997 0.3474 0.7403 −0.6630 0.3474 −0.4438 −0.1999 0.3474 0.6442 −0.5805 0.3474 −0.3515 −0.2965 0.3474 0.5493 −0.4967 0.3474 −0.2564 −0.3895 0.3474 0.4556 −0.4117 0.3474 −0.1585 −0.4791 0.3474 0.3629 −0.3255 0.3474 −0.0579 −0.5654 0.3474 0.2711 −0.2383 0.3474 0.0452 −0.6485 0.3474 0.1803 −0.1502 0.3474 0.1509 −0.7285 0.3474 0.0902 −0.0611 0.3474 0.2590 −0.8054 0.3474 0.0009 0.0288 0.3474 0.3696 −0.8792 0.3474 −0.0876 0.1195 0.3474 0.4827 −0.9500 0.3474 −0.1754 0.2110 0.3474 0.5981 −1.0178 0.3474 −0.2624 0.3032 0.3474 0.7115 −1.0804 0.3474 −0.3458 0.3930 0.3474 0.8225 −1.1382 0.3474 −0.4257 0.4803 0.3474 0.9306 −1.1917 0.3474 −0.5022 0.5649 0.3474 1.0358 −1.2411 0.3474 −0.5754 0.6469 0.3474 1.1377 −1.2869 0.3474 −0.6452 0.7262 0.3474 1.2361 −1.3295 0.3474 −0.7118 0.8027 0.3474 1.3309 −1.3693 0.3474 −0.7757 0.8760 0.3474 1.4220 −1.4064 0.3474 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0.2926 1.0465 0.9722 −0.4936 1.0465 −0.5562 0.2017 1.0465 0.8790 −0.4224 1.0465 −0.4673 0.1102 1.0465 0.7832 −0.3480 1.0465 −0.3756 0.0218 1.0465 0.6881 −0.2728 1.0465 −0.2814 −0.0633 1.0465 0.5938 −0.1967 1.0465 −0.1849 −0.1451 1.0465 0.5002 −0.1197 1.0465 −0.0861 −0.2237 1.0465 0.4073 −0.0419 1.0465 0.0148 −0.2992 1.0465 0.3150 0.0368 1.0465 0.1179 −0.3717 1.0465 0.2234 0.1161 1.0465 0.2230 −0.4413 1.0465 0.1322 0.1961 1.0465 0.3301 −0.5080 1.0465 0.0414 0.2765 1.0465 0.4392 −0.5720 1.0465 −0.0490 0.3574 1.0465 0.5501 −0.6334 1.0465 −0.1391 0.4385 1.0465 0.6627 −0.6926 1.0465 −0.2291 0.5199 1.0465 0.7728 −0.7477 1.0465 −0.3159 0.5988 1.0465 0.8799 −0.7990 1.0465 −0.3994 0.6752 1.0465 0.9840 −0.8470 1.0465 −0.4797 0.7492 1.0465 1.0849 −0.8916 1.0465 −0.5568 0.8207 1.0465 1.1826 −0.9332 1.0465 −0.6305 0.8899 1.0465 1.2768 −0.9719 1.0465 −0.7010 0.9566 1.0465 1.3675 −1.0081 1.0465 −0.7685 1.0206 1.0465 1.4545 −1.0420 1.0465 −0.8302 1.0788 1.0465 1.5338 −1.0723 1.0465 −0.8862 1.1315 1.0465 1.6054 −1.0992 1.0465 −0.9364 1.1785 1.0465 1.6690 −1.1229 1.0465 −0.9808 1.2198 1.0465 1.7288 −1.1449 1.0465 −1.0196 1.2552 1.0465 1.7806 −1.1638 1.0465 −1.0530 1.2846 1.0465 1.8205 −1.1783 1.0465 −1.0824 1.3087 1.0465 1.8525 −1.1899 1.0465 −1.1080 1.3277 1.0465 1.8766 −1.1980 1.0465 −1.1302 1.3418 1.0465 1.8953 −1.1956 1.0465 −1.1489 1.3514 1.0465 1.9040 −1.1897 1.0465 −1.1640 1.3571 1.0465 1.9084 −1.1845 1.0465 −1.1759 1.3595 1.0465 1.9102 −1.1816 1.0465 −1.1860 1.3597 1.0465 1.9110 −1.1801 1.0465 −1.1939 1.3580 1.0465 −1.2025 1.4593 1.3961 1.9201 −0.9918 1.3961 −1.2074 1.4552 1.3961 1.9204 −0.9910 1.3961 −1.2124 1.4482 1.3961 1.9210 −0.9895 1.3961 −1.2163 1.4382 1.3961 1.9219 −0.9865 1.3961 −1.2184 1.4256 1.3961 1.9228 −0.9802 1.3961 −1.2187 1.4085 1.3961 1.9220 −0.9703 1.3961 −1.2163 1.3867 1.3961 1.9137 −0.9547 1.3961 −1.2107 1.3597 1.3961 1.8943 −0.9408 1.3961 −1.2015 1.3275 1.3961 1.8674 −0.9234 1.3961 −1.1882 1.2902 1.3961 1.8338 −0.9017 1.3961 −1.1707 1.2474 1.3961 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1.3961 −0.1328 0.5765 1.3961 0.6814 −0.5257 1.3961 −0.2236 0.6550 1.3961 0.7907 −0.5786 1.3961 −0.3112 0.7309 1.3961 0.8972 −0.6279 1.3961 −0.3957 0.8044 1.3961 1.0005 −0.6738 1.3961 −0.4770 0.8754 1.3961 1.1007 −0.7166 1.3961 −0.5550 0.9442 1.3961 1.1977 −0.7563 1.3961 −0.6298 1.0106 1.3961 1.2912 −0.7933 1.3961 −0.7013 1.0746 1.3961 1.3811 −0.8279 1.3961 −0.7697 1.1360 1.3961 1.4674 −0.8603 1.3961 −0.8323 1.1921 1.3961 1.5461 −0.8894 1.3961 −0.8889 1.2427 1.3961 1.6170 −0.9152 1.3961 −0.9395 1.2881 1.3961 1.6800 −0.9379 1.3961 −0.9843 1.3279 1.3961 1.7392 −0.9591 1.3961 −1.0233 1.3623 1.3961 1.7906 −0.9773 1.3961 −1.0568 1.3909 1.3961 1.8301 −0.9912 1.3961 −1.0861 1.4144 1.3961 1.8617 −1.0024 1.3961 −1.1118 1.4328 1.3961 1.8855 −1.0102 1.3961 −1.1339 1.4465 1.3961 1.9041 −1.0079 1.3961 −1.1524 1.4558 1.3961 1.9128 −1.0021 1.3961 −1.1674 1.4612 1.3961 1.9172 −0.9969 1.3961 −1.1792 1.4636 1.3961 1.9190 −0.9940 1.3961 −1.1892 1.4637 1.3961 1.9197 −0.9925 1.3961 −1.1970 1.4619 1.3961 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2.4448 −1.2137 1.7997 2.4448 1.9504 −0.5255 2.4448 −1.2170 1.7897 2.4448 1.9512 −0.5225 2.4448 −1.2186 1.7772 2.4448 1.9521 −0.5162 2.4448 −1.2182 1.7604 2.4448 1.9509 −0.5065 2.4448 −1.2149 1.7389 2.4448 1.9416 −0.4916 2.4448 −1.2081 1.7127 2.4448 1.9217 −0.4787 2.4448 −1.1974 1.6814 2.4448 1.8948 −0.4622 2.4448 −1.1824 1.6453 2.4448 1.8611 −0.4414 2.4448 −1.1629 1.6040 2.4448 1.8174 −0.4143 2.4448 −1.1385 1.5559 2.4448 1.7670 −0.3829 2.4448 −1.1091 1.5010 2.4448 1.7134 −0.3493 2.4448 −1.0741 1.4396 2.4448 1.6531 −0.3114 2.4448 −1.0332 1.3721 2.4448 1.5864 −0.2689 2.4448 −0.9861 1.2990 2.4448 1.5131 −0.2220 2.4448 −0.9323 1.2209 2.4448 1.4367 −0.1725 2.4448 −0.8739 1.1412 2.4448 1.3573 −0.1205 2.4448 −0.8108 1.0602 2.4448 1.2749 −0.0659 2.4448 −0.7426 0.9781 2.4448 1.1894 −0.0087 2.4448 −0.6692 0.8951 2.4448 1.1010 0.0512 2.4448 −0.5904 0.8114 2.4448 1.0097 0.1140 2.4448 −0.5057 0.7271 2.4448 0.9157 0.1796 2.4448 −0.4151 0.6426 2.4448 0.8190 0.2482 2.4448 −0.3214 0.5607 2.4448 0.7228 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1.7491 2.4448 1.8597 −0.5277 2.4448 −1.0879 1.7713 2.4448 1.8912 −0.5379 2.4448 −1.1139 1.7887 2.4448 1.9149 −0.5453 2.4448 −1.1362 1.8014 2.4448 1.9334 −0.5436 2.4448 −1.1549 1.8099 2.4448 1.9422 −0.5379 2.4448 −1.1700 1.8146 2.4448 1.9466 −0.5329 2.4448 −1.1817 1.8164 2.4448 1.9484 −0.5300 2.4448 −1.1916 1.8161 2.4448 1.9492 −0.5285 2.4448 −1.1992 1.8140 2.4448 −1.1988 1.9404 3.1439 1.9517 −0.3506 3.1439 −1.2033 1.9361 3.1439 1.9520 −0.3498 3.1439 −1.2078 1.9290 3.1439 1.9525 −0.3484 3.1439 −1.2110 1.9190 3.1439 1.9534 −0.3454 3.1439 −1.2125 1.9066 3.1439 1.9541 −0.3392 3.1439 −1.2119 1.8899 3.1439 1.9527 −0.3296 3.1439 −1.2085 1.8686 3.1439 1.9429 −0.3153 3.1439 −1.2017 1.8426 3.1439 1.9227 −0.3030 3.1439 −1.1907 1.8117 3.1439 1.8957 −0.2870 3.1439 −1.1755 1.7761 3.1439 1.8620 −0.2670 3.1439 −1.1556 1.7354 3.1439 1.8182 −0.2408 3.1439 −1.1305 1.6882 3.1439 1.7677 −0.2104 3.1439 −1.1002 1.6344 3.1439 1.7140 −0.1780 3.1439 −1.0643 1.5743 3.1439 1.6536 −0.1412 3.1439 −1.0223 1.5083 3.1439 1.5868 −0.1001 3.1439 −0.9742 1.4368 3.1439 1.5134 −0.0546 3.1439 −0.9194 1.3605 3.1439 1.4369 −0.0066 3.1439 −0.8601 1.2827 3.1439 1.3574 0.0439 3.1439 −0.7960 1.2035 3.1439 1.2749 0.0970 3.1439 −0.7271 1.1233 3.1439 1.1894 0.1528 3.1439 −0.6531 1.0422 3.1439 1.1011 0.2113 3.1439 −0.5737 0.9603 3.1439 1.0098 0.2725 3.1439 −0.4888 0.8778 3.1439 0.9159 0.3366 3.1439 −0.3982 0.7950 3.1439 0.8191 0.4037 3.1439 −0.3047 0.7147 3.1439 0.7229 0.4714 3.1439 −0.2091 0.6375 3.1439 0.6272 0.5398 3.1439 −0.1116 0.5633 3.1439 0.5319 0.6089 3.1439 −0.0123 0.4923 3.1439 0.4371 0.6786 3.1439 0.0887 0.4242 3.1439 0.3426 0.7489 3.1439 0.1915 0.3590 3.1439 0.2487 0.8198 3.1439 0.2958 0.2966 3.1439 0.1551 0.8912 3.1439 0.4018 0.2368 3.1439 0.0619 0.9632 3.1439 0.5092 0.1795 3.1439 −0.0308 1.0357 3.1439 0.6180 0.1246 3.1439 −0.1232 1.1087 3.1439 0.7282 0.0721 3.1439 −0.2151 1.1823 3.1439 0.8359 0.0233 3.1439 −0.3035 1.2540 3.1439 0.9410 −0.0219 3.1439 −0.3885 1.3236 3.1439 1.0432 −0.0639 3.1439 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1.9473 3.8430 1.9523 −0.2644 3.8430 −1.2070 1.9308 3.8430 1.9505 −0.2549 3.8430 −1.2032 1.9098 3.8430 1.9399 −0.2413 3.8430 −1.1958 1.8842 3.8430 1.9195 −0.2298 3.8430 −1.1843 1.8539 3.8430 1.8923 −0.2145 3.8430 −1.1682 1.8190 3.8430 1.8583 −0.1953 3.8430 −1.1474 1.7793 3.8430 1.8142 −0.1703 3.8430 −1.1210 1.7334 3.8430 1.7633 −0.1413 3.8430 −1.0893 1.6811 3.8430 1.7092 −0.1102 3.8430 −1.0517 1.6227 3.8430 1.6484 −0.0750 3.8430 −1.0082 1.5587 3.8430 1.5810 −0.0356 3.8430 −0.9585 1.4894 3.8430 1.5072 0.0082 3.8430 −0.9021 1.4153 3.8430 1.4302 0.0543 3.8430 −0.8413 1.3398 3.8430 1.3502 0.1030 3.8430 −0.7760 1.2629 3.8430 1.2672 0.1543 3.8430 −0.7059 1.1848 3.8430 1.1813 0.2083 3.8430 −0.6310 1.1057 3.8430 1.0925 0.2650 3.8430 −0.5511 1.0258 3.8430 1.0010 0.3246 3.8430 −0.4659 0.9453 3.8430 0.9067 0.3870 3.8430 −0.3752 0.8643 3.8430 0.8097 0.4525 3.8430 −0.2819 0.7856 3.8430 0.7132 0.5187 3.8430 −0.1868 0.7095 3.8430 0.6173 0.5857 3.8430 −0.0899 0.6365 3.8430 0.5219 0.6534 3.8430 0.0088 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−0.9949 9.4360 −0.9390 1.2520 9.4360 1.8330 −1.0025 9.4360 −0.9617 1.2712 9.4360 1.8558 −1.0082 9.4360 −0.9812 1.2860 9.4360 1.8732 −1.0102 9.4360 −0.9975 1.2969 9.4360 1.8821 −1.0060 9.4360 −1.0106 1.3042 9.4360 1.8865 −1.0014 9.4360 −1.0210 1.3085 9.4360 1.8881 −0.9987 9.4360 −1.0302 1.3106 9.4360 1.8888 −0.9972 9.4360 −1.0377 1.3103 9.4360 −1.0126 1.3370 9.7855 1.8626 −1.0504 9.7855 −1.0168 1.3327 9.7855 1.8628 −1.0497 9.7855 −1.0196 1.3252 9.7855 1.8632 −1.0482 9.7855 −1.0206 1.3153 9.7855 1.8637 −1.0453 9.7855 −1.0198 1.3035 9.7855 1.8634 −1.0393 9.7855 −1.0171 1.2880 9.7855 1.8596 −1.0307 9.7855 −1.0118 1.2681 9.7855 1.8456 −1.0214 9.7855 −1.0037 1.2439 9.7855 1.8252 −1.0116 9.7855 −0.9923 1.2151 9.7855 1.7980 −0.9984 9.7855 −0.9772 1.1815 9.7855 1.7641 −0.9818 9.7855 −0.9582 1.1428 9.7855 1.7203 −0.9596 9.7855 −0.9344 1.0976 9.7855 1.6700 −0.9336 9.7855 −0.9060 1.0461 9.7855 1.6167 −0.9052 9.7855 −0.8728 0.9882 9.7855 1.5572 −0.8724 9.7855 −0.8347 0.9243 9.7855 1.4916 −0.8351 9.7855 −0.7916 0.8543 9.7855 1.4201 −0.7929 9.7855 −0.7432 0.7783 9.7855 1.3461 −0.7476 9.7855 −0.6910 0.7001 9.7855 1.2696 −0.6990 9.7855 −0.6350 0.6196 9.7855 1.1908 −0.6472 9.7855 −0.5753 0.5370 9.7855 1.1098 −0.5920 9.7855 −0.5114 0.4526 9.7855 1.0266 −0.5334 9.7855 −0.4435 0.3667 9.7855 0.9414 −0.4713 9.7855 −0.3715 0.2796 9.7855 0.8540 −0.4057 9.7855 −0.2950 0.1914 9.7855 0.7645 −0.3366 9.7855 −0.2164 0.1052 9.7855 0.6759 −0.2663 9.7855 −0.1359 0.0210 9.7855 0.5880 −0.1950 9.7855 −0.0533 −0.0611 9.7855 0.5008 −0.1229 9.7855 0.0314 −0.1411 9.7855 0.4142 −0.0501 9.7855 0.1183 −0.2189 9.7855 0.3283 0.0235 9.7855 0.2077 −0.2943 9.7855 0.2432 0.0980 9.7855 0.2997 −0.3670 9.7855 0.1591 0.1736 9.7855 0.3946 −0.4368 9.7855 0.0759 0.2502 9.7855 0.4921 −0.5035 9.7855 −0.0063 0.3279 9.7855 0.5917 −0.5668 9.7855 −0.0877 0.4065 9.7855 0.6932 −0.6267 9.7855 −0.1683 0.4861 9.7855 0.7931 −0.6816 9.7855 −0.2454 0.5637 9.7855 0.8913 −0.7318 9.7855 −0.3192 0.6394 9.7855 0.9873 −0.7775 9.7855 −0.3897 0.7129 9.7855 1.0809 −0.8190 9.7855 −0.4571 0.7842 9.7855 1.1718 −0.8567 9.7855 −0.5215 0.8531 9.7855 1.2600 −0.8909 9.7855 −0.5830 0.9196 9.7855 1.3451 −0.9219 9.7855 −0.6416 0.9836 9.7855 1.4271 −0.9498 9.7855 −0.6949 1.0423 9.7855 1.5022 −0.9739 9.7855 −0.7431 1.0954 9.7855 1.5701 −0.9943 9.7855 −0.7861 1.1430 9.7855 1.6307 −1.0117 9.7855 −0.8240 1.1850 9.7855 1.6877 −1.0272 9.7855 −0.8572 1.2211 9.7855 1.7373 −1.0400 9.7855 −0.8859 1.2512 9.7855 1.7755 −1.0495 9.7855 −0.9111 1.2761 9.7855 1.8062 −1.0569 9.7855 −0.9330 1.2963 9.7855 1.8292 −1.0623 9.7855 −0.9519 1.3120 9.7855 1.8467 −1.0643 9.7855 −0.9677 1.3236 9.7855 1.8557 −1.0601 9.7855 −0.9805 1.3315 9.7855 1.8600 −1.0554 9.7855 −0.9908 1.3363 9.7855 1.8616 −1.0527 9.7855 −0.9999 1.3389 9.7855 1.8623 −1.0512 9.7855 −1.0074 1.3390 9.7855 −0.9717 1.4214 10.1351 1.8213 −1.1046 10.1351 −0.9762 1.4173 10.1351 1.8216 −1.1039 10.1351 −0.9796 1.4099 10.1351 1.8220 −1.1024 10.1351 −0.9813 1.4000 10.1351 1.8224 −1.0994 10.1351 −0.9813 1.3879 10.1351 1.8221 −1.0933 10.1351 −0.9796 1.3719 10.1351 1.8182 −1.0847 10.1351 −0.9756 1.3514 10.1351 1.8042 −1.0752 10.1351 −0.9688 1.3263 10.1351 1.7837 −1.0651 10.1351 −0.9591 1.2964 10.1351 1.7564 −1.0516 10.1351 −0.9459 1.2613 10.1351 1.7223 −1.0344 10.1351 −0.9291 1.2207 10.1351 1.6783 −1.0115 10.1351 −0.9078 1.1733 10.1351 1.6279 −0.9845 10.1351 −0.8821 1.1192 10.1351 1.5746 −0.9550 10.1351 −0.8522 1.0583 10.1351 1.5151 −0.9209 10.1351 −0.8177 0.9908 10.1351 1.4496 −0.8820 10.1351 −0.7783 0.9170 10.1351 1.3784 −0.8378 10.1351 −0.7339 0.8367 10.1351 1.3047 −0.7904 10.1351 −0.6858 0.7540 10.1351 1.2287 −0.7394 10.1351 −0.6340 0.6687 10.1351 1.1506 −0.6850 10.1351 −0.5784 0.5810 10.1351 1.0705 −0.6270 10.1351 −0.5188 0.4915 10.1351 0.9883 −0.5654 10.1351 −0.4551 0.4003 10.1351 0.9042 −0.5001 10.1351 −0.3871 0.3075 10.1351 0.8181 −0.4312 10.1351 −0.3145 0.2134 10.1351 0.7301 −0.3586 10.1351 −0.2397 0.1213 10.1351 0.6431 −0.2847 10.1351 −0.1626 0.0312 10.1351 0.5569 −0.2098 10.1351 −0.0830 −0.0568 10.1351 0.4714 −0.1339 10.1351 −0.0010 −0.1428 10.1351 0.3869 −0.0572 10.1351 0.0835 −0.2265 10.1351 0.3033 0.0206 10.1351 0.1707 −0.3079 10.1351 0.2210 0.0996 10.1351 0.2611 −0.3867 10.1351 0.1399 0.1799 10.1351 0.3542 −0.4622 10.1351 0.0600 0.2614 10.1351 0.4497 −0.5337 10.1351 −0.0188 0.3440 10.1351 0.5473 −0.6013 10.1351 −0.0965 0.4276 10.1351 0.6471 −0.6652 10.1351 −0.1733 0.5123 10.1351 0.7455 −0.7234 10.1351 −0.2465 0.5950 10.1351 0.8425 −0.7763 10.1351 −0.3164 0.6755 10.1351 0.9376 −0.8245 10.1351 −0.3831 0.7538 10.1351 1.0308 −0.8681 10.1351 −0.4466 0.8297 10.1351 1.1217 −0.9077 10.1351 −0.5073 0.9032 10.1351 1.2103 −0.9434 10.1351 −0.5651 0.9740 10.1351 1.2963 −0.9756 10.1351 −0.6201 1.0422 10.1351 1.3794 −1.0045 10.1351 −0.6701 1.1046 10.1351 1.4555 −1.0291 10.1351 −0.7151 1.1613 10.1351 1.5245 −1.0499 10.1351 −0.7554 1.2120 10.1351 1.5860 −1.0674 10.1351 −0.7910 1.2567 10.1351 1.6440 −1.0828 10.1351 −0.8222 1.2951 10.1351 1.6945 −1.0955 10.1351 −0.8492 1.3272 10.1351 1.7334 −1.1047 10.1351 −0.8731 1.3539 10.1351 1.7646 −1.1118 10.1351 −0.8940 1.3755 10.1351 1.7880 −1.1170 10.1351 −0.9120 1.3925 10.1351 1.8057 −1.1187 10.1351 −0.9272 1.4052 10.1351 1.8146 −1.1143 10.1351 −0.9397 1.4139 10.1351 1.8188 −1.1096 10.1351 −0.9497 1.4193 10.1351 1.8204 −1.1068 10.1351 −0.9587 1.4225 10.1351 1.8210 −1.1054 10.1351 −0.9663 1.4231 10.1351 −0.9488 1.4777 10.2892 1.7955 −1.1349 10.2892 −0.9536 1.4738 10.2892 1.7958 −1.1341 10.2892 −0.9573 1.4665 10.2892 1.7962 −1.1326 10.2892 −0.9594 1.4565 10.2892 1.7967 −1.1296 10.2892 −0.9600 1.4444 10.2892 1.7963 −1.1235 10.2892 −0.9588 1.4282 10.2892 1.7925 −1.1148 10.2892 −0.9556 1.4073 10.2892 1.7785 −1.1051 10.2892 −0.9497 1.3818 10.2892 1.7578 −1.0948 10.2892 −0.9410 1.3512 10.2892 1.7303 −1.0810 10.2892 −0.9290 1.3153 10.2892 1.6962 −1.0635 10.2892 −0.9135 1.2738 10.2892 1.6520 −1.0402 10.2892 −0.8937 1.2252 10.2892 1.6014 −1.0125 10.2892 −0.8698 1.1697 10.2892 1.5479 −0.9823 10.2892 −0.8419 1.1071 10.2892 1.4884 −0.9473 10.2892 −0.8097 1.0378 10.2892 1.4229 −0.9073 10.2892 −0.7726 0.9618 10.2892 1.3517 −0.8619 10.2892 −0.7307 0.8793 10.2892 1.2782 −0.8131 10.2892 −0.6851 0.7941 10.2892 1.2024 −0.7605 10.2892 −0.6359 0.7062 10.2892 1.1246 −0.7044 10.2892 −0.5829 0.6158 10.2892 1.0449 −0.6446 10.2892 −0.5260 0.5234 10.2892 0.9633 −0.5810 10.2892 −0.4649 0.4291 10.2892 0.8798 −0.5137 10.2892 −0.3996 0.3332 10.2892 0.7945 −0.4426 10.2892 −0.3297 0.2358 10.2892 0.7074 −0.3676 10.2892 −0.2573 0.1403 10.2892 0.6213 −0.2914 10.2892 −0.1824 0.0468 10.2892 0.5360 −0.2141 10.2892 −0.1050 −0.0446 10.2892 0.4517 −0.1358 10.2892 −0.0249 −0.1340 10.2892 0.3684 −0.0565 10.2892 0.0578 −0.2212 10.2892 0.2863 0.0240 10.2892 0.1434 −0.3061 10.2892 0.2056 0.1058 10.2892 0.2323 −0.3884 10.2892 0.1264 0.1890 10.2892 0.3238 −0.4672 10.2892 0.0484 0.2735 10.2892 0.4179 −0.5419 10.2892 −0.0283 0.3591 10.2892 0.5145 −0.6126 10.2892 −0.1038 0.4459 10.2892 0.6135 −0.6794 10.2892 −0.1782 0.5337 10.2892 0.7117 −0.7403 10.2892 −0.2491 0.6195 10.2892 0.8085 −0.7957 10.2892 −0.3166 0.7030 10.2892 0.9039 −0.8460 10.2892 −0.3809 0.7843 10.2892 0.9975 −0.8916 10.2892 −0.4421 0.8630 10.2892 1.0892 −0.9329 10.2892 −0.5004 0.9392 10.2892 1.1786 −0.9702 10.2892 −0.5559 1.0127 10.2892 1.2653 −1.0035 10.2892 −0.6088 1.0833 10.2892 1.3490 −1.0333 10.2892 −0.6567 1.1481 10.2892 1.4257 −1.0585 10.2892 −0.6998 1.2069 10.2892 1.4952 −1.0798 10.2892 −0.7384 1.2595 10.2892 1.5574 −1.0975 10.2892 −0.7726 1.3058 10.2892 1.6159 −1.1131 10.2892 −0.8026 1.3456 10.2892 1.6668 −1.1259 10.2892 −0.8287 1.3788 10.2892 1.7062 −1.1351 10.2892 −0.8518 1.4065 10.2892 1.7377 −1.1423 10.2892 −0.8721 1.4291 10.2892 1.7614 −1.1474 10.2892 −0.8896 1.4468 10.2892 1.7793 −1.1492 10.2892 −0.9046 1.4600 10.2892 1.7885 −1.1449 10.2892 −0.9169 1.4692 10.2892 1.7930 −1.1400 10.2892 −0.9268 1.4750 10.2892 1.7946 −1.1372 10.2892 −0.9357 1.4784 10.2892 1.7953 −1.1356 10.2892 −0.9433 1.4792 10.2892 −0.9059 1.5902 10.5472 1.7452 −1.1921 10.5472 −0.9110 1.5866 10.5472 1.7454 −1.1914 10.5472 −0.9154 1.5795 10.5472 1.7458 −1.1899 10.5472 −0.9184 1.5695 10.5472 1.7463 −1.1868 10.5472 −0.9199 1.5572 10.5472 1.7460 −1.1806 10.5472 −0.9200 1.5406 10.5472 1.7422 −1.1717 10.5472 −0.9183 1.5191 10.5472 1.7281 −1.1616 10.5472 −0.9142 1.4927 10.5472 1.7072 −1.1510 10.5472 −0.9076 1.4609 10.5472 1.6794 −1.1366 10.5472 −0.8979 1.4235 10.5472 1.6449 −1.1183 10.5472 −0.8850 1.3801 10.5472 1.6002 −1.0940 10.5472 −0.8682 1.3292 10.5472 1.5492 −1.0650 10.5472 −0.8478 1.2710 10.5472 1.4954 −1.0333 10.5472 −0.8237 1.2053 10.5472 1.4355 −0.9966 10.5472 −0.7956 1.1325 10.5472 1.3699 −0.9544 10.5472 −0.7630 1.0526 10.5472 1.2986 −0.9065 10.5472 −0.7259 0.9657 10.5472 1.2252 −0.8548 10.5472 −0.6852 0.8758 10.5472 1.1497 −0.7992 10.5472 −0.6409 0.7829 10.5472 1.0724 −0.7396 10.5472 −0.5930 0.6873 10.5472 0.9935 −0.6761 10.5472 −0.5412 0.5894 10.5472 0.9129 −0.6085 10.5472 −0.4853 0.4893 10.5472 0.8306 −0.5369 10.5472 −0.4250 0.3873 10.5472 0.7468 −0.4613 10.5472 −0.3600 0.2836 10.5472 0.6613 −0.3816 10.5472 −0.2924 0.1818 10.5472 0.5769 −0.3007 10.5472 −0.2220 0.0818 10.5472 0.4935 −0.2186 10.5472 −0.1487 −0.0161 10.5472 0.4111 −0.1354 10.5472 −0.0725 −0.1120 10.5472 0.3302 −0.0510 10.5472 0.0067 −0.2059 10.5472 0.2510 0.0349 10.5472 0.0891 −0.2975 10.5472 0.1736 0.1222 10.5472 0.1749 −0.3866 10.5472 0.0979 0.2111 10.5472 0.2636 −0.4720 10.5472 0.0237 0.3013 10.5472 0.3553 −0.5533 10.5472 −0.0489 0.3929 10.5472 0.4502 −0.6303 10.5472 −0.1200 0.4856 10.5472 0.5481 −0.7030 10.5472 −0.1899 0.5795 10.5472 0.6458 −0.7694 10.5472 −0.2561 0.6712 10.5472 0.7427 −0.8298 10.5472 −0.3189 0.7606 10.5472 0.8387 −0.8846 10.5472 −0.3784 0.8474 10.5472 0.9334 −0.9343 10.5472 −0.4350 0.9315 10.5472 1.0263 −0.9791 10.5472 −0.4887 1.0129 10.5472 1.1168 −1.0191 10.5472 −0.5398 1.0914 10.5472 1.2048 −1.0549 10.5472 −0.5883 1.1669 10.5472 1.2899 −1.0866 10.5472 −0.6323 1.2360 10.5472 1.3680 −1.1133 10.5472 −0.6717 1.2988 10.5472 1.4388 −1.1356 10.5472 −0.7071 1.3549 10.5472 1.5023 −1.1541 10.5472 −0.7385 1.4042 10.5472 1.5620 −1.1704 10.5472 −0.7662 1.4467 10.5472 1.6141 −1.1834 10.5472 −0.7903 1.4822 10.5472 1.6543 −1.1929 10.5472 −0.8119 1.5119 10.5472 1.6865 −1.2001 10.5472 −0.8309 1.5361 10.5472 1.7107 −1.2053 10.5472 −0.8476 1.5552 10.5472 1.7291 −1.2068 10.5472 −0.8619 1.5695 10.5472 1.7382 −1.2022 10.5472 −0.8738 1.5796 10.5472 1.7426 −1.1973 10.5472 −0.8836 1.5861 10.5472 1.7443 −1.1944 10.5472 −0.8924 1.5901 10.5472 1.7449 −1.1929 10.5472 −0.9001 1.5913 10.5472 −0.8494 1.7419 10.8670 1.6782 −1.2673 10.8670 −0.8550 1.7387 10.8670 1.6785 −1.2665 10.8670 −0.8604 1.7320 10.8670 1.6789 −1.2650 10.8670 −0.8646 1.7221 10.8670 1.6794 −1.2618 10.8670 −0.8675 1.7095 10.8670 1.6791 −1.2555 10.8670 −0.8693 1.6925 10.8670 1.6754 −1.2463 10.8670 −0.8697 1.6703 10.8670 1.6612 −1.2356 10.8670 −0.8682 1.6426 10.8670 1.6399 −1.2244 10.8670 −0.8644 1.6093 10.8670 1.6116 −1.2092 10.8670 −0.8581 1.5699 10.8670 1.5764 −1.1899 10.8670 −0.8489 1.5241 10.8670 1.5310 −1.1641 10.8670 −0.8364 1.4702 10.8670 1.4792 −1.1334 10.8670 −0.8206 1.4084 10.8670 1.4247 −1.0996 10.8670 −0.8013 1.3389 10.8670 1.3642 −1.0604 10.8670 −0.7782 1.2616 10.8670 1.2980 −1.0153 10.8670 −0.7516 1.1766 10.8670 1.2264 −0.9639 10.8670 −0.7210 1.0840 10.8670 1.1528 −0.9083 10.8670 −0.6869 0.9881 10.8670 1.0775 −0.8483 10.8670 −0.6493 0.8888 10.8670 1.0007 −0.7840 10.8670 −0.6081 0.7863 10.8670 0.9226 −0.7153 10.8670 −0.5631 0.6811 10.8670 0.8431 −0.6422 10.8670 −0.5139 0.5734 10.8670 0.7624 −0.5647 10.8670 −0.4604 0.4635 10.8670 0.6804 −0.4829 10.8670 −0.4022 0.3515 10.8670 0.5970 −0.3966 10.8670 −0.3410 0.2414 10.8670 0.5149 −0.3090 10.8670 −0.2767 0.1331 10.8670 0.4339 −0.2203 10.8670 −0.2092 0.0267 10.8670 0.3543 −0.1304 10.8670 −0.1384 −0.0776 10.8670 0.2767 −0.0389 10.8670 −0.0642 −0.1800 10.8670 0.2014 0.0542 10.8670 0.0134 −0.2802 10.8670 0.1284 0.1491 10.8670 0.0948 −0.3783 10.8670 0.0574 0.2456 10.8670 0.1801 −0.4733 10.8670 −0.0115 0.3436 10.8670 0.2692 −0.5638 10.8670 −0.0786 0.4430 10.8670 0.3620 −0.6496 10.8670 −0.1440 0.5437 10.8670 0.4588 −0.7306 10.8670 −0.2076 0.6455 10.8670 0.5558 −0.8044 10.8670 −0.2674 0.7449 10.8670 0.6528 −0.8717 10.8670 −0.3239 0.8417 10.8670 0.7494 −0.9327 10.8670 −0.3771 0.9357 10.8670 0.8453 −0.9878 10.8670 −0.4273 1.0268 10.8670 0.9397 −1.0373 10.8670 −0.4749 1.1148 10.8670 1.0319 −1.0815 10.8670 −0.5198 1.1998 10.8670 1.1219 −1.1206 10.8670 −0.5623 1.2814 10.8670 1.2091 −1.1551 10.8670 −0.6010 1.3561 10.8670 1.2894 −1.1841 10.8670 −0.6362 1.4235 10.8670 1.3623 −1.2081 10.8670 −0.6674 1.4840 10.8670 1.4277 −1.2278 10.8670 −0.6949 1.5373 10.8670 1.4893 −1.2450 10.8670 −0.7192 1.5834 10.8670 1.5431 −1.2587 10.8670 −0.7406 1.6219 10.8670 1.5846 −1.2685 10.8670 −0.7598 1.6542 10.8670 1.6179 −1.2759 10.8670 −0.7772 1.6806 10.8670 1.6430 −1.2812 10.8670 −0.7926 1.7016 10.8670 1.6618 −1.2826 10.8670 −0.8060 1.7175 10.8670 1.6712 −1.2777 10.8670 −0.8174 1.7287 10.8670 1.6756 −1.2726 10.8670 −0.8269 1.7361 10.8670 1.6773 −1.2697 10.8670 −0.8357 1.7408 10.8670 1.6779 −1.2681 10.8670 −0.8434 1.7426 10.8670

It will be appreciated that the airfoil 105 disclosed in the above scalable TABLE 1 may be non-scaled, scaled up, or scaled down geometrically for use in other or similar turbine/compressor designs. Consequently, the coordinate values set forth in TABLE 1 may be non-scaled, scaled upwardly, or scaled downwardly such that the general airfoil profile shape remains unchanged. A scaled version of the coordinates in TABLE 1 would be represented by X, Y, and Z coordinate values of TABLE 1, with the X, Y, and Z non-dimensional coordinate values converted to inches or millimeters (or any suitable dimensional system), multiplied or divided by a constant number. The constant number may be a fraction, decimal fraction, integer or mixed number.

The disclosed airfoil shape thus may increase reliability and may be specific to the machine conditions and specifications. The airfoil shape provides a unique profile to achieve (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade or vane loadings. The disclosed loci of points allow the gas turbine and the compressor or any other suitable turbine/compressor to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil may be adopted as long as (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled compressor.

The airfoil 105 described herein thus improves overall compressor efficiency. Specifically, the airfoil 105 may provide the desired turbine/compressor efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 105 also meets all aeromechanics, loading and stress requirements.

It should be apparent that the foregoing relates only to certain embodiments of the present application and the resultant patent. Numerous changes and modifications may be made herein by one of ordinary skill in the art without departing from the general spirit and scope of the invention as defined by the following claims and the equivalents thereof. 

We claim:
 1. An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.
 2. The article of manufacture according to claim 1, wherein the article of manufacture comprises an airfoil.
 3. The article of manufacture according to claim 1, wherein the article of manufacture comprises a stator vane configured for use with a compressor.
 4. The article of manufacture according to claim 1, wherein the airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to an airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to an airfoil surface location.
 5. The article of manufacture according to claim 1, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 6. The article of manufacture according to claim 1, wherein a height of the article of manufacture is about 1 inch to about 20 inches (about 2.54 centimeters to about 50.8 centimeters).
 7. An article of manufacture having a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape, the X, Y, and Z coordinate values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil profile.
 8. The article of manufacture according to claim 7, wherein the article of manufacture comprises an airfoil.
 9. The article of manufacture according to claim 7, wherein the article of manufacture comprises a stator vane configured for use with a compressor.
 10. The article of manufacture according to claim 7, wherein the suction-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a suction-side airfoil surface location.
 11. The article of manufacture according to claim 7, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 12. The article of manufacture according to claim 7, wherein a height of the article of manufacture is about 1 inch to about 20 inches (about 2.54 centimeters to about 50.8 centimeters).
 13. The article of manufacture according to claim 7, further comprising the article of manufacture having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y, and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete pressure-side airfoil shape, the X, Y, and Z values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil.
 14. A compressor comprising a plurality of stator vanes, each of the stator vanes including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape.
 15. The compressor according to claim 14, wherein the suction-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a suction-side airfoil surface location.
 16. The compressor according to claim 14, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 17. The compressor according to claim 14, wherein a height of each stator vane is about 1 inch to about 20 inches (about 2.54 centimeters to about 50.8 centimeters).
 18. The compressor according to claim 14, further comprising each of the plurality of stator vanes having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y, and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by the number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete pressure-side airfoil shape.
 19. The compressor according to claim 18, wherein the pressure-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a pressure-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a pressure-side airfoil surface location.
 20. The compressor according to claim 18, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number. 